1. Electromagnetics (ENGR 367)
Magnetic Materials & Magnetization

2. Introduction
Question: Why do some materials respond to magnetic fields, while others do not?
Answer: Magnetic materials have a property known as Magnetization as quantified in the relative permeability constant (r).

3. Description of Magnetic Material Properties
For accurate quantitative prediction: Quantum Theory is required
For qualitative description:
Orbital Mechanics Model suffices

4. Orbital Mechanics Model
Atom has electrons that orbit around its nucleus making a miniature current loop that results in an orbital magnetic moment
Electron spins around its own axis to produce a significant spin magnetic moment

5. Orbital Mechanics Model
The relative contribution of the magnetic moments of each atom and the molecular makeup of a material classifies it as
Diamagnetic
Paramagnetic
Ferromagnetic
Antiferromagnetic
Ferrimagnetic
Superparamagnetic
Any atom with a magnetic moment in the presence of an applied magnetic field will experience a torque that tends to align it

6. Domain
Definition:
a region within a ferromagnetic material having a large dipole moment due to collections of associated atoms with uncompensated spin moments
Shape, size & direction of moment:
varies between neighboring regions within a crude sample that cancels the effect overall
See also magnetic dipole moments and domains of ferromagnetic materials as illustrated in Fig WW pp. 139, 140.

7. Alignment of Magnetic Domains
may be achieved by an applied magnetic field
Upon removal of the external magnetic field, domains do not all return to their original state and thus exhibit a magnetic history known as hysteresis (an interesting & practical effect unique to ferromagnetic materials)
Examples: Ferromagnetic elements & compounds
Fe, Ni, Co, BiMn, CuMnSn, etc.
See also nonlinear Magnetization curve in Fig WW p. 141

8. Other Examples of Magnetic Materials Each Class
Class of Magnetic Material
Ex’s: Elements & Compounds
Diamagnetic
Bi, H, He, NaCl, Au, Cu, Si, Ge, etc.
Paramagnetic
K, O, etc.
Antiferromagnetic
MnO, NiO, FeS, CoCl2, etc.
Ferrimagnetic
Fe3O4 (iron oxide magnetite),
NiFe2O4 (nickel ferrite), etc.
Superparamagnetic
Ferromagnetic particles in a nonferromagnetic matrix

9. Qualitative Summary of Magnetic Material Properties
Class
morbvs. mspin
Bint vs. Bappl
Comments
Dia-
morb = -mspin
<
weak effect
Para-
morb+mspin small
>
Antiferro-
<< 
int. canc.
Ferro-
>>
Domains!
Ferri-
High resist.
Superpara-
Matrix

10. Applications of Magnetic Materials
Ferromagnetic Materials: Permanent Magnets, Magnetic Data Storage, etc.
Ferrimagnetic Materials: Ferrites commonly used for transformer and/or toroid cores due to their higher resistance that reduces eddy currents that cause ohmic loss
Superparamagnetic: used to create recording tape for audio or video application

11. Magnetization Quantified
Approach: define Amperian (bound) current
Associated with bound charges of electrons in atoms locked into lattice structure of a material
Magnetic dipole moment of each individual charge
For n dipoles per unit volume
Magnetization: magnetic dipole moment per unit vol.

12. Bound versus Free Current Forms of A.C.L.
Mathematic Expressions:
Bound versus Free
Note:
Ib depends on the number and alignment of the miniature magnetic dipoles along the closed path

13. Bound & Free Currents Combined
Total Current
Free Current
General Relation for B versus H

14. Linear Isotropic Magnetic Media (e.g., paramagnetic, diamagnetic)
Magnetization
Magnetic Flux Density

15. Nonlinear & Anisotropic Materials (e.g., ferromagnetic)
If magnetization (M) responds nonlinearly to an imposed magnetic field (H) such as for a ferromagnetic polycrystalline material
relation still applies, but. . .
the parameters m and r will not be constant material properties since H vs. M is nonlinear
If linear and homogeneous, but anisotropic as for a ferromagnetic single crystal then

16. Example of Magnetization Calculation
Exercise 3 (D9.6, Hayt & Buck, 7/e, p. 281):
Find:
Given: a)

17. Example of Magnetization Calculation
Exercise 3 (continued)
Find:
Given: b)

18. Example of Magnetization Calculation
Exercise 3 (continued)
Find:
Given: c)

19. Summary Forces on moving charge in a magnetic field may result in
Forces on current carrying conductors
Torques on current loops
Magnetization results from miniature bound current loops of electrons with
Orbital magnetic moments
Spin magnetic moments

20. Summary
Different classes of materials exist, some have weaker and some stronger magnetic effects
The permeability constant () indicates the magnetization and magnetic effects of a linear, isotropic material
Some ferromagnetic materials have practical nonlinear or anisotropic effects
Applications of magnetic materials include: permanent magnets, data storage, motors, generators, transformer/toroid cores, etc.

21. References
Hayt & Buck, Engineering Electromagnetics, 7th edition, McGraw Hill: New York, 2006.
Wentworth, Fundamentals of Electromagnetics with Engineering Applications, John Wiley & Sons: 2005.